Yeovil, who came into the game on the back of three straight wins, always looked happy to take a point and showed little ambition in a game that lacked any real poise or purpose.
The first half was an instantly forgettable affair, although Orient created the better chances. Paul Terry, playing against his former club, almost headed the O's into the lead on 12 minutes, but his powerful effort flew just wide.
Home defender Tamika Mkandawire was denied by Yeovil goalkeeper Steve Mildenhall when he saved his header at the foot of a post following Jason Demetriou's left-wing corner.
Demetriou then shot inches wide from the edge of the box, but the closest Orient came to breaking the deadlock was when Charlie Daniels whipped in a free-kick from the left and top scorer Adam Boyd deflected the ball onto a post.
Little was seen of Yeovil as an attacking force with skipper Terry Skiverton having their only first-half effort on target but his tame header was easily saved by Stuart Nelson in the home goal.
The second half was no better, although Yeovil boss Russell Slade threw Lloyd Owusu into the fray and played with two strikers. But neither side found any sort of rhythm as Orient struggled to break down the Glovers' resolute defence.
Mkandawire went close with another header, while Yeovil had two half-chances as James Walker and Paul Warner had shots on target.
But it was Orient substitute Efe Echanomi who came closest to winning the game with a couple of efforts in the final ten minutes.